Our proposal focuses on the development of a class of new and novel nonparametric likelihood methods for statistical inference to handle problems encountered during a recent clinical trial, Oral Health and Ventilator- Associated Pneumonia-A Phase III Randomized Single Center Trial (Grant number: 1 R01DE14685 - 01A1). A total of 175 patients in an intensive care unit (ICU) were treated with chlorhexidine oral rinse once or twice per day or with a placebo control, and followed until they were discharged. Outcome variables include oral colonization by target micro-organisms, the dental Plaque Index score and diagnostic variables for pneumonia. Three major issues that warrant the statistical investigation were as follows. 1) A data attrition problem exists in the data sets with respect to variables such as the Plaque Index and bacterial colonization scores in the oral cavity. In longitudinal studies, the attrition of the experimental units is a major problem and currently nonparametric likelihood methods have not been well developed to solve the problem. In particular, for oral health research, multiple outcomes from a patient and the corresponding correlation structure further complicate the data analysis. 2) General outcome measurements are subject to instrument sensitivity where values are not available because of the limit of detection and subject to measurement errors. 3) There is systematic missingness in the data due to the fact that one variable is observed only if the other variable satisfies a certain condition such as exceeding a threshold (e.g., CPIS and triggering collections of BAL). This project proposes the development of statistical inference methods using the nonparametric likelihood approaches to test multiple groups in the presence of incomplete data or data attrition. Some available parametric likelihood (PL) approaches can address the missing data problem, however, for incomplete data, these parametric assumptions cannot be tested using standard goodness-of-fit tests. We will develop a series of nonparametric likelihood methods relevant to the structure of incomplete data, where missing patterns are taken into account. These new methods will allow the users to avoid strong distributional assumptions by using a nonparametric approach. We will pay special attention toward utilizing the maximum information retained in the pattern of incomplete data. This novel approach will provide more powerful and accurate analyses. This approach is also immediately useful for the analysis of oral health data in general, since common dental caries or periodontal disease datasets are riddled with similar missing data problems. To help transfer of the methodology, we plan to develop user-friendly software. The investigators also plan, in the context of this proposal, to train students and medical investigators with the correct and powerful approaches to the given challenges. Application of these methods will enable flexible and powerful inference in clinical investigations. If fully successful, we believe that the proposed methods have a great potential to be adopted as a primary statistical tool that changes the practice of study planning for various clinical areas.